You cannot delete a reference from the RefCheck database, but you can remove it by simply not citing it. To remove a reference, simply delete the citation in the manuscript. No changes to other in-text citation need to be made, in particular it is not necessary to renumber any references. For example, if you no longer want to cite reference 3, delete the in-text citation (eg, ) from the Word file, without changing  and subsequent citations.
During typesetting, our scripts will omit that reference and automatically renumber all subsequent references and in-text citations in the final proof.
Note that after copyediting (in the proofreading/galleys stage), no changes to the order of references can be made without additional costs (as this requires manual re-ordering), so during copyediting it is your last chance to edit the references.